In this paper, we address portfolio optimisation when stock prices follow general Lévy processes in the context of a pension accumulation scheme. The optimal portfolio weights are obtained in quasi-closed form and the optimal consumption in closed form. To solve the optimisation problem, we show how to switch back and forth between the stochastic differential and standard exponentials of the Lévy processes. We apply this procedure to both the Variance Gamma process and a Lévy process whose arrival rate of jumps exponentially decreases with size. We show through a numerical example that when jumps, and therefore asymmetry and leptokurtosis, are suitably taken into account, then the optimal portfolio share of the risky asset is around half that obtained in the Gaussian framework.

We solve in closed form the problem of an agent who maximises his inter-temporal lifetime utility. The agent is subject to the so-called longevity risk, i.e. his force of mortality is stochastic. His utility is additively separable on leisure (while working) and consumption. Consumer’s preferences belong to the Hyperbolic Absolute Risk Aversion family, with a subsistence consumption level. The individual optimally chooses labour supply, consumption, and portfolio allocation. We study these optimal choices when the agent has access to a complete financial market, where he can trade in longevity-linked securities. He can also contribute to a personal pension scheme. A calibrated application shows that the optimal demand for the longevity-linked assets crucially depends on the stages of the agent’s life and his wage profiles. This observation opens up the possibility of longevity risk transfers across individuals with heterogeneous characteristics.